The frame needs to have the BB30 specific bottom bracket shell so you can't install it on a regular frame. The adaptor lets you use a standard BB and crankset on a SI specific frame but since the SI shell is bigger, the other way around is not possible.

The SI cranks use what Cannondale calls the BB30 standard and they finally opened it and now allow other companies to use it for free. Specialized started to use the standard on some road bikes and the team bikes (Christoph and Liam at least) also use it, which leads us to believe they will adopt the standard on some mountain bikes next year, probably a S-Works only thing. So the SI cranks can be installed on those Specialized and the Specialized road crank is installable on Cannondale with the SI BB frames. You can get more info on BB30 here.